NIST Technical Note 1876 

MicroChar 

An Application for Quantitative Analysis of 

Cement and Clinker Microstructure Images 

Jeffrey W. Bullard 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1876 
 

 

 

NIST Technical Note 1876 

MicroChar 

An Application for Quantitative Analysis of 

Cement and Clinker Microstructure Images 

Jeffrey W. Bullard 

Materials and Structural Systems Division 

Engineering Laboratory 

http://dx.doi.org/10.6028/NIST.TN.1876 

April 2015 

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Willie May, Acting Under Secretary of Commerce for Standards and Technology and Acting Director
 

 

 

 

 

 

Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. 

Such identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1876 

Natl. Inst. Stand. Technol. Tech. Note 1876, 20 pages (April 2015) 

CODEN: NTNOEF

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1876
 

 

 

 

 

 

 

 

 

 

 

Abstract

Accurate quantitative data on cement and clinker microstructure images can prove valuable for monitoring and controlling the manufacturing of cement-based powders. Furthermore, quantitative characterization of microstructure is an essential input to microstructure-based computer models of cementitious material processing and properties. This document describes the use and operating principles of

MicroChar, a computer application for automatically calculating a range of microstructural properties

from an indexed 2D image. Among the properties calculated are the volume fraction, mass fraction,

and surface area fraction of each phase in the image, as well as two-point correlation functions for

quantifying the spatial distribution of the phases throughout the structure. The application also enables the user to package the data obtained on cement powders for uploading to the Virtual Cement

and Concrete Testing Laboratory Consortium (VCCTL) software.

Keywords: Building technology; cement; clinker; microstructure; computer modeling

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Contents

1 Introduction 1
 

1.1 Disclaimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
 

1.2 Intent and Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
 

1.3 Notation Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
 

2 Software Prerequisites 2
 

3 Installation 2
 

3.1 Installing on Microsoft Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
 

3.1.1 Terms of Use Agreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
 

3.1.2 Installation Folder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
 

3.1.3 Ready to Install . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
 

3.2 Installing on Mac OS X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
 

4 Uninstalling MicroChar 4
 

4.1 Uninstalling on Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
 

4.2 Uninstalling on Mac OS X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
 

5 Using MicroChar 5
 

5.1 Image Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
 

5.2 The Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
 

5.3 Cement Powder Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
 

5.3.1 VCCTL Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
 

5.4 Clinker Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
 

5.5 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
 

6 Calculation Principles and Algorithms 11
 

6.1 Volume Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
 

6.2 Mass Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
 

6.3 Area Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
 

6.4 Two-point correlation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
 

6.4.1 Properties of two-point correlation functions . . . . . . . . . . . . . . . . . . . . . 13
 

6.4.2 Calculation of two-point correlation functions . . . . . . . . . . . . . . . . . . . . . 15
 

7 Summary 15
 

References 15
 

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1 INTRODUCTION
 

1 Introduction

This document provides guidance for using MicroChar, subject to Disclaimer in Section 1.1, a computer

application for performing quantitative analysis of cement and clinker microstructural images. The application consists of a graphical user interface and the underlying computer models and programs that

allow users to open indexed microstructure images, to identify the constituent mineral phases, to determine mass, volume, and surface area fractions of those phases, and to characterize the spatial distribution

of those phases in terms of two-point correlation functions. Optionally, for cement powder microstructure

images, the user may provide additional information and package the resulting data in a collection of files

suitable for direct uploading to the Virtual Cement and Concrete Testing Laboratory 9.5 (VCCTL) software

platform.

1.1 Disclaimer

This software was developed at the National Institute of Standards and Technology (NIST) by employees

of the Federal Government in the course of their official duties. Pursuant to Title 17 Section 105 of the

United States Code this software is not subject to copyright protection and is in the public domain. NIST

assumes no responsibility whatsoever for the use of MicroChar by other parties, and makes no guarantees,

expressed or implied, about its quality, reliability, or any other characteristic. NIST would appreciate

acknowledgment, such as an appropriate citation in a publication, if the software is used.

The U.S. Department of Commerce makes no warranty, expressed or implied, to users of MicroChar,

and accepts no responsibility for its use. Users of MicroChar assume sole responsibility under Federal law

for determining the appropriateness of its use in any particular application; for any conclusions drawn

from the results of its use; and for any actions taken or not taken as a result of analyses performed using

these tools. All results should be critically evaluated by an informed user.

1.2 Intent and Use

The computer program described in this guide constitutes a prototype application for quantitative image

analysis of cement powder and clinker microstructures. It has been compiled from the best knowledge and

understanding currently available, but has some limitations that must be understood and considered by

the user. MicroChar is intended for use by persons competent in the field of cement-based materials and

having some familiarity with computers.

1.3 Notation Conventions

Throughout this guide, the following text conventions will be used:

• italicized text will indicate

– words on a MicroChar window (for example, the Execute button);

– key combinations Ctrl-O to indicate the keyboard combination of Control plus O).

• Courier font will be used to indicate

– a file name: mycement.img or disrealnew.exe;

– the location of a folder or file: C:“Users“user“mycement;

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3 INSTALLATION
 

– web addresses: http://oracle.com

• Bold text will indicate an important note or warning that the user must heed (for example, Beware

that calculating correlation functions can take a considerable amount of time).

• Words in all capital letters will be used to denote variables in file names or user names for which the

user must supply the correct value.

2 Software Prerequisites

The following requirements must be met for successful installation and running of MicroChar:

• Operating system: Microsoft Windows 7∗ or Mac OS X 10.9∗ or later. Other versions of Windows,

such as XP, Vista, or Windows 8, or earlier versions of Mac OS X may or may not be compatible

with MicroChar.

• A minimum of 2 GB RAM and minimum free hard disk space of 1 GB for long-term use of the

software.

3 Installation

3.1 Installing on Microsoft Windows

To install MicroChar on Windows, download and then double click on the installer file (MicroChar1.0-windows-installer.exe) icon to the Desktop. A series of windows will guide you through the

installation process.

3.1.1 Terms of Use Agreement

This dialog requires you to acknowledge the software disclaimer, which has language identical to that in

Section 1.1. If you accept the disclaimer agreement, you can proceed with the installation by pressing the

Next button. Otherwise, the installation will be cancelled.

∗Certain commercial equipment and/or materials are identified in this report in order to adequately specify the experimental

procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and

Technology, nor does it imply that the equipment and/or materials used are necessarily the best available for the purpose.

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3 INSTALLATION
 

3.1.2 Installation Folder

You may install MicroCharin any location on your computer, provided that you have the adequate read/write

permissions. The default path and folder is MicroChar located in C:“Program Files. You may accept

that default or change it to another location. However, the final folder on the path must be named

MicroChar The software may not work properly if it is not installed in a folder named MicroChar.

3.1.3 Ready to Install

The next dialog box indicates that the software is ready to install. Click the Next button to begin the

installation.

The installation should finish within a few seconds, after which a window will notify you that the

installation is complete. Close this window by clicking on the Finish button.

When the installation is complete, a new shortcut icon for MicroChar should appear on your Desktop,

and MicroChar should also be listed in the Start Menu. Either one can be used to launch the application.

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4 UNINSTALLING MICROCHAR
 

3.2 Installing on Mac OS X

Double click the compressed disk image file, MicroChar.dmg, which will mount the disk image and

open a window on your Desktop. The application may be installed anywhere by dragging the circular

application icon to a file folder. A shortcut to the Applications folder is provided in the mounted disk

image for convenience.

Once the application is installed, eject the disk image by locating its icon on the Desktop and dragging

it to the Trash on the Dock.

4 Uninstalling MicroChar

4.1 Uninstalling on Windows

The easiest way to remove from a Windows computer is to launch the uninstaller, which can be found in

the Start Menu.

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5 USING MICROCHAR
 

A dialog box will ask if you are sure you want to uninstall the application. Click Yes to start removing the

software. The entire processshould finish within a few seconds, after which another window will appear to

announce that the removal is complete. This removes all the installed files, including the Desktop shortcut

icon and the Start Menu items.

4.2 Uninstalling on Mac OS X

Drag the application from its installed folder to the Trash to remove it from a Mac OS X computer.

5 Using MicroChar

5.1 Image Requirements

MicroChar works with a 2D indexed image file. The details of preparaing such an image file from scanning

electron microscope data are beyond the scope of this document. Instructions for doing so can be found

in a recent report [1]. The indexed image must meet the following formatting requirements:

1. The file must contain ASCII text.

2. There must be no header information of any kind in the image.

3. Each row of the image corresponds to one line of text in the file, uninterrupted by new lines or

carriage returns.

4. The number of characters in a single line corresponds to the number of columns in the 2D image.

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5 USING MICROCHAR
 

5. Only tab characters or spaces should separate the characters within a line.

6. Each character in a line must be a positive integer that can be used to uniquely identify the phase

located in the pixel at the corresponding row and column of the image.

Images meeting these requirements can be readily produced using ImageJ, a freely available image

processing software package [2]. In addition to the formatting requirements, the image resolution (in

units of μm/pixel) should be known.

Launch MicroChar by double clicking its icon, which will open the main window.

Mousing over an item in the window will display its tooltip. For more context-specific information,

click on the blue question mark icon in the toolbar and then click on the window item to reveal more

information about it.

5.2 The Toolbar

The toolbar at the top of the main window provides quick access to common tasks, as described in Table 1.

To begin a session, open the indexed image using the toolbar (or type Ctrl-O), and navigate to the

desired image file. The application works equally well on indexed images either of clinker or of powdered

cement embedded in epoxy, but it analyzes the void space and identifies perimeteris differently for the two

kinds of images.

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5 USING MICROCHAR
 

Table 1: Toolbar actions.
 

Icon Action Keyboard Shortcut

Open an indexed image Ctrl-O

Save calculations and

associated files Ctrl-S

Interrupt a calculation

and erase intermediate

data files

Close the main window

and exit the application

Obtain context-specific

information about any

item by clicking on it

Ctrl-Q

Shift-F1

5.3 Cement Powder Images

For cement powder images, ensure that the Clinker Image checkbox is unchecked. Specify the image

resolution in the text field, in terms of the width of a single pixel in micrometer (μm) units. The pixel

dimension should be known at the time that the microstructure image is acquired experimentally, and is

necessary to associate a length scale with the two-point correlation functions that will be calculated if

the corresponding checkbox is activated below the resolution text field. Note: Calculating correlation

functions can take considerable time, up to 30 min or more depending on how many phases are

in the image.

The remaining items in the window, which are disabled by default, are related to data needed to create

a cement data package for the Virtual Cement and Concrete Testing Laboratory (VCCTL) modeling software [3, 4]. Activating the VCCTL Package checkbox will enable these fields, and during the calculations

it will prepare a data folder that can be directly uploaded in VCCTL 9.5 to add a new cement for modeling.

5.3.1 VCCTL Data

For preparing VCCTL cement data packages, enter the appropriate information about the cement powder

in the following data fields:

•	 VCCTL Name. Enter a name for the cement, which will be assigned to the VCCTL data package

folder and all the files therein.

•	 Gypsum. Enter the mass percent of gypsum (calcium sulfate dihydrate) in the cement, on a total

solids basis.

•	 Bassanite. Enter the mass percent of bassanite (calcium sulfate hemihydrate) in the cement, on a

total solids basis.

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5 USING MICROCHAR
 

•	 Anhydrite. Enter the mass percent of soluble anhydrite (calcium sulfate) in the cement, on a total

solids basis.

•	 PSD File. Enter the full path and file name of an ASCII text file containing the particle size distribution data for the cement. Use the Browse button to navigate to the approriate file. The file must

be formatted as two-column ASCII text, with the left column being the particle diameter in μm and

the right column being the probability density function (differential volume fraction for the corresponding size bin). A tab or space(s) may separate the two columns. If a suitable file is not available,

a default file will be created and stored for the cement. It can be edited later.

•	 Na2O/Readily Soluble. Enter the mass percent of sodium oxide in the cement, as determined by X-ray

fluorescence spectroscopy, on a total solids basis. In the text field to the right, enter the mass percent

of sodium (assumed to be sodium oxide) that is readily soluble, on a total solids basis.

•	 K2O/ReadilySoluble. Enter the mass percent of potassium oxide in the cement, as determined by

X-ray fluorescence spectroscopy, on a total solids basis. In the text field to the right, enter the mass

percent of potassium (assumed to be potassium oxide) that is readily soluble, on a total solids basis.

•	 Desc. Enter a brief description of the type of cement, its application, date received, or other pertinent

information.

•	 Source. Enter a brief description of the source of the material.

•	 Fineness. Enter the powder’s specific surface area (m2 kg−1).

•	 Method. Select the experimental method used to measure the powder’s specific surface area:

–	 Blaine (air permeability test)

–	 PSD Analysis (inference from particle size distribution assuming spherical particles)

–	 BET Analysis (multipoint nitrogen adsorption isotherms)

–	 Other

Calculations begin by clicking the Execute button at the bottom of the window. The program reads the

image file and records all the phase index numbers. When these have been collected, the user is prompted

to associate each index with a known phase. A default collection is offered, but each phase can be manually

assigned by selecting the desired phase from the pulldown menu next to each phase id found in the image.

Click the OK button when the desired selections have been made.

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5 USING MICROCHAR
 

Remaining calculations will be automatically performed. The progress is displayed approximately in

the progress bar beneath the Execute button, and relevant messages about the calculations are displayed in

the status bar at the bottom of the window. When the calculations are finished, the status bar will provide a

text prompt to save the work. Note: If a VCCTL package is requested, the program will calculate required

two-point correlation functionsfor the clinker minerals, whether or not the Calculate Correlation Functions

checkbox is activated. However, the VCCTL correlation functions cover a much smaller domain and do

not take more than a few seconds each to calculate.

Saving to a user-defined data folder is done by clicking on the blue diskette icon in the toolbar (or

typing Ctrl-S), and then navigating to the desired location and typing the name of a new data folder to

store the results.

5.4 Clinker Images

Activate the Clinker image checkbox only if the opened image is a clinker nodule; otherwise leave it

unchecked. Specify the image resolution in the text field, in terms of the width of a single pixel in micrometer (μm) units. The pixel dimension should be known at the time that the microstructure image is

acquired experimentally, and is necessary to associate a length scale with the correlation functions that

will be calculated if the corresponding checkbox is activated. Clinker images cannot be prepared as a

VCCTL package, so the rest of the data items in the window can be skipped.

Calculations begin by clicking the Execute button at the bottom of the window. In the same manner as

for cement images already described, the program reads the image file, records the phase index numbers,

and provides a dialog to prompt for the phase associated with each number. Click the OK button when

the desired selections have been made.

5.5 Calculations

MicroChar performs the following sequence of operations on both clinker and cement powder images:

1. Small, isolated voids and cracks within grains are removed so that they will not falsely contribute

to the perimeter of any phase (clinker images only).†

2. The area of each phase is calculated and normalized by the total solid area to yield its area fraction

on a total solids basis.

3. The mass fraction of each phase, on a total solids basis, is calculated from the area fractions and

knowledge of the density of each phase.

4. The perimeter of each phase is calculated. For clinker images, the perimeter is defined as the boundary of the given phase with any other phase; for cement images, the perimeter is defined as the

boundary of the given phase only with interparticle porosity, because such boundaries determine

the reactive surface area with water.

5. False color PNG images are created of (a) the microstructure and (b) the phase perimeters.

6. Two-point correlation functions, also known as autocorrelation functions in the field of signal processing, are calculated for each phase (only if the checkbox was activated).

†Such “internal” voids and cracks might actually bridge to the surface in the direction perpendicular to the image field, but in

the absence of further information we treat them as wholly interior to the grain.

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5 USING MICROCHAR
 

7. The program displays a window summarizing the results of the calculations for each phase.
 

8. The program halts and prompts you to save your work if you wish, which you may do by clicking

on the disk icon in the tool bar or by typing Ctrl-S.

After saving your work, at least four files are always placed in the saved folder:

1. A file with extension ’pfc’‡, which contain the mass, area, and perimeter fractions of each phase in

the microstructure on a total solids basis;

2. One file with extension ’png’ and another with extension ’surf.png’. These are the color PNG images,

the first showing the microstructure and second showing the phase perimeters in outline.

‡The extension ’pfc’ is an acronym for phase fractions of cement (or clinker).

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6 CALCULATION PRINCIPLES AND ALGORITHMS
 

3. A file named ColorKey.png, which displays a key to the different colors in the microstructure

images created by the program.

Additionally, if the Calculate Correlation Functions checkbox was activated, a collection of files, each

ending with a different phase name, will be produced to store the two-point correlation function results

for that phase.

6 Calculation Principles and Algorithms

This section briefly describes the principles used to perform the several image analyses described in the

previous section.

6.1 Volume Fraction

The volume fraction§ of each solid phase is measured by simple point counting of pixels. Let Ni be the

number of pixels of phase i in a microstructure image having n solid phases. Then the volume fraction vi

on a total solids basis is

Ni

v = i = 1,2,. . . ,n (1) i

n 

n

Nk

k=1

6.2 Mass Fraction

The massfraction of each phase, on a totalsolids mass basis, is computed directly from the volume fractions

by weighting each phase’s volume fraction by its density. The densities assumed for each phase are shown

§Some confusion could arise over the use of the terms “volume” and “area” in image analysis. This document adopts the

mathematical concept of volume as a measure of the size of a subspace having the same dimensionality as the parent space.

Therefore, a volume in 3D space is a 3D quantity, and a volume in 2D (such as a microstructure image) is a 2D quantity. Likewise,

area is the measure of a having dimension one fewer than the parent space. An area in 3D is a 2D quantity, and an area in 2D

is a 1D quantity, which some might prefer to call a perimeter. However, we retain volume and area primarily because of their

correspondence with volume and area of the actual 3D microstructure.

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6 CALCULATION PRINCIPLES AND ALGORITHMS
 

Table 2: Density assumed for each solid phase.
 

Phase Name Density (103 kg m−3) Phase Name Density (103 kg m−3)

Alite 3.21 Belite 3.28

Aluminate 3.04 Ferrite 3.73

Arcanite 2.66 Thenardite 2.68

Gypsum(a)

Calcite(b)

2.32

2.71

Lime

Periclase

3.31

3.78

Silica 2.65 Kaolin 2.60

CAS(c) 2.77 Slag 2.20

Other 2.60

(a) “Gypsum” is used here as a generic name for the various hydrated and

anhydrous calcium sulfate phasesfound in cementitious powders, and the

assumed density is therefore an approximate value.

(b) “Calcite” as used here could include some magnesium impurities more

properly identified as a dolomitic mineral, but the density assumed is for

pure calcite.

(c) “CAS” represents a generic calcium aluminosilicate glass similar in composition to some glassesin fly ash materials; the density is an approximate

value typical of aluminosilicate glasses.

in Table 2. The mass fraction, mi , of phase i is therefore

ρivi

mi = i = 1,2,. . . ,n (2)

n 

n

ρkvk

k=1

6.3 Area Fraction

The area fraction, ai , of solid phase i is defined here as the fraction of the combined interface area that has

phase i one one or the other side of it. For clinker images, an interface is the boundary between any two

dissimilar phases. For cement powder images, an interface is the boundary between one solid phase and

the interparticle porosity.

In a digitized image, interface area is measured by counting pixel edges. For example, a single square

pixel of phase i embedded in a different phase has an interface area of four edge lengths because the pixel

has four edges. Therefore, the area fraction of phase i is the sum of all the pixel edges of i shared with

another phase, divided by the sum of all the pixel edge lengths defining all the interfaces in the image,

N

ni

Lij

j=1

ai = n Nk(3)

n n Lk j

k=1 j=1

where Lij is the number of face edges of the j-th pixel of phase i lying at an interface, and the denominator

includes a sum over all n phases in the microstructure image.

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6 CALCULATION PRINCIPLES AND ALGORITHMS
 

The definition given in Eq. (3) effectively double-counts all the interface area because each edge at an

interface is counted once for each of the two phases sharing that edge. This means that, for example, in

a two-phase image, each phase is calculated to have an area fraction of 0.5, even though each phase is

present at all of the interface edges. One might argue that in such an image the area fraction should be 1.0

for both phases, but this convention would have the disadvantage of not being normalized to unity.

Correlation function data file Plot

6.4 Two-point correlation functions

6.4.1 Properties of two-point correlation functions

The two-point correlation function for a phase, S2 (r), is the probability that two randomly selected points

in the image, separated by a distance r, both lie within that phase. In random composite materials, S2 has

some generic features that can be used to characterize the spatial distribution of the phase. For example,

when r = 0, the points coincide; the probability of a randomly selected point lying within a phase in a 2D

image is equal to the area fraction, φ, of that phase, on a total area basis. Therefore, S2 (0) = φ, that is, the

y-intercept of the plot is equal to the phase’s area fraction. A second property of S2 (r), which will not be

proven here, is that its limiting slope as r → 0 is directly proportional to the phase’s boundary length per

unit area, Σ. In particular, for granular media the exact relation can be shown to be [5]

dS2 Σ lim = − (4) r→0+ dr 4

A third property of S2 is that, at sufficiently large distances between the two points in a random microstructure, the phase identity of each pointshould be independent of the other. In other words, the phase

distribution should be uncorrelated at large distances. When two events are statistically independent, the

joint probability is equal to the product of the (unconditional) individual event probabilities. As stated earlier, the probability of a single point lying within a phase is the phase’s area fraction, φ, so S2 at sufficiently

large distances should converge to φ2.

Examination of the plot below shows that S2 (0) = 0.4457 for alite, which therefore is alite’s area

fraction on a total image area basis¶.

¶Note that this fraction is somewhat lower than the value reported in the pfc data file for the same image because the latter

value is normalized to the total solids area only.

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6 CALCULATION PRINCIPLES AND ALGORITHMS
 

Furthermore, the slope atr = 0 for alite is approximately −0.0158 μm−1, which provides a semiquantitative

indication of the specific boundary area of alite in the image. Finally, the plot indicates that S2 for neither

alite nor belite appears to be converging to φ2, which is 0.198 for alite and 0.1024 for belite. This can be

interpreted to mean that the spatial distribution of each phase is still somewhat correlated at distances as

large as 200 μm.

The plot below showsthe two-point correlation functionsforthe minority phases arcanite and periclase

in a clinker material.

This plot highlights two other features of two-point correlation functions. First, the correlation functions

appear to be converging to values of about 10−3 for periclase and about 10−4 for arcanite at distances

no greater than about 100 μm. At r = 0, the values of φ for periclase and arcanite are 0.0337 and 0.0046,

respectively. Squaring these values gives 0.0011 for periclase and 0.00002 for arcanite, both values of which

are reasonably close to the long-distance values. Therefore, both periclase and arcanite are concluded to

lose any spatial correlation at distances of about 100 μm.

The second feature of the two-point correlation functions in this plot is the appearance of a local minimum at short distances followed by a small-amplitude oscillation in the curves. The periodic local minima

are characteristic of granular media and of non-overlapping domains in composites, such as periclase and

arcanite. In such materials, the distance at which the first local minimum occurs corresponds to about

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REFERENCES
 

half the average equivalent radius of the domain, and the distance at which the following local maximum

happens corresponds to the average domain spacing in the microstructure [5]. Inspection of the plot suggests that the average equivalent radius of periclase and arcanite domains is about 31 μm and about 18 μm,

respectively. Likewise, the average domain spacings of periclase and arcanite are about 40 μm and about

27 μm, respectively.

6.4.2 Calculation of two-point correlation functions

For a rectangular digitized images, the two-point correlation function can be conveniently calculated by

convolution, by which, conceptually, two identical copies are overlaid and displaced relative to each other

by a prescribed number of pixels in the x direction and a prescribed number of pixels in the y direction,

and then counting the pixels that have the same phase located at the same position in the original image

as in the displaced image [6, 7]. In an image of M × N pixels, the 2D two-point correlation function is

M

2 2 −x N −y I (i,j)I (i + x,j + y) S2 (x,y) = (5) (M − x)(N − y) i=1 j=1

where I (x,y) = 1 if the pixel at location (x,y) contains the phase of interest and I (x,y) = 0 otherwise. In a

statistically isotropic microstructure, the 2D correlation function can be converted to be a 1D function of

distance only [6, 7]

2

2r 1 πi

S2 (r) = S2 r,	 (6) 2r + 1 4r i=0

where, for a given angle θi = πi/4r, S2 (r cos θi ,r sinθi ) is obtained by bilinear interpolation from the

values of S (x,y).

7	 Summary

MicroChar is a straightforward application for performing quantitative phase analysis on indexed 2D images of cement powder or clinker microstructures. The kinds of data obtained from MicroChar can provide

valuable information for monitoring and controlling the manufacturing of cement-based powders. The application can also facilitate the packaging of cement powder data in a form that can be uploaded to the

VCCTL software package for simulating 3D cement microstructures, hydration, and engineering properties [3, 4].

References

[1]	 P. E. Stutzman, J. W. Bullard, and P. Feng. Quantitative Imaging of Clinker and Cement Microstructure.

Technical Note. Washington, D.C.: National Institute of Standards and Technology, 2015.

[2]	 ImageJ: Image Processing and Analysis in Java. Accessed: 2015-03-16. url: http://imagej.nih.

gov/ij/.

[3]	 VCCTL Software.Accessed: 2015-03-16. url: http://www.nist.gov/el/building materials/

evcctl.cfm.

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[4] Jeffrey W. Bullard. Virtual Cement and Concrete Testing Laboratory: Version 9.5 User Guide. Special

Publication SP 1173. Washington, D.C.: National Institute of Standards and Technology, May 2014.

[5] J. G. Berryman and S. C. Blair.“Use of Digital Image Analysisto Estimate Fluid Permeability of Porous

Materials: Application of Two-Point Correlation Functions”. In: J. Appl. Phys. 60.6 (1986), pp. 1930–

1938.

[6] J. G. Berryman. “Measurement of Spatial Correlation Functions Using Image Processing Techniques”.

In: J. Appl. Phys. 57.7 (1985), pp. 2374–2384.

[7] D. P. Bentz.“Three-Dimensional Computer Simulation of Portland Cement Hydration and Microstructure Development”. In: J. Am. Ceram. Soc. 80.1 (1997), pp. 3–21.

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